Conventionally, jitter is often used as an index in the evaluation of quality of signals reproduced from an optical disc. However, in view of a recent trend to detect data with PRML (Partial Response Maximum Likelihood) to achieve high density recording, Jitter, which varies with time, does not make a suitable quality index. Another evaluation index used is the bit error rate of PRML data detection results, which however requires measurement of a lot of sample bits and is likely to be affected by defects caused by scratches on the disc and other factors.
With such a background, T. Perkins, “A Window Margin Like Procedure for Evaluating PRML Channel Performance,” IEEE Transactions on Magnetics, Vol. 31, No. 2, 1995, pp. 1109-1114 suggests a quality evaluation method for reproduced signals called “SAM (Sequenced Amplitude Margin).”
The concept of SAM will be described in reference to FIGS. 33 and 34. An example is taken here in which a bit sequence recorded by (1,7) RLL (Run Length Limited) encoding is decoded by PRML based on PR (1,2,1).
As shown in FIG. 33, the reproduced signal waveform for an ideal 1T mark which reflects PR (1,2,1) and is free of distortion and noise has a 1:2:1 sample level ratio for each channel clock. “T” is the time equivalent to one cycle of a channel clock. An “nT mark” is a mark which has a length equivalent to nT. The reproduced signal waveform for a mark longer than or equal to 2T is obtainable through superimposition of waveforms like this one for a 1T mark. For example, the sample level ratio is 1:3:3:1 for a 2T mark, 1:3:4:3:1 for a 3T mark, and 1:3:4:4:3:1 for a 4T mark. An ideal reproduced signal waveform for a given bit sequence is thus known. There are five ideal sample levels: 0, 1, 2, 3, and 4. For convenience, the sample levels are normalized for maximum amplitudes of ±1. The five normalized, ideal sample levels are −1, −0.5, 0, +0.5, and +1.
Viterbi decoding is employed here as a specific way to realize PRML decoding. Let us examine the trellis diagram shown in FIG. 34 which is drawn for the Viterbi decoding with the sample levels specified above. In FIG. 34, S(00), S(01), S(10), and S(11) denote different states. State S(00) indicates that the preceding bit is a 0 and the current bit is a 0. State S(01) indicates that the preceding bit is a 0 and the current bit is a 1. State S(10) indicates that the preceding bit is a 1 and the current bit is a 0. State S(11) indicates that the preceding bit is a 1 and the current bit is a 1.
A line connecting one state to another is called a branch, indicating a state transition. For example, the S(00)-to-S(01) branch represents a “001” bit sequence. In FIG. 34, letters a to f are allocated to identify individual branches. The identifying letters are accompanied by an ideal waveform level expected in the state transition. For example, the ideal level for “a” is −1 because the letter represents a “000” bit sequence. The ideal level for “b” is −0.5 because the letter represents a “100” bit sequence. The S(01)-to-S(10) and S(10)-to-S(01) branches are missing from the diagram, because the “010” and “101” bit sequences cannot occur due to the d=1 Run Length Limit in the (1,7) RLL code which is a modulation scheme where the shortest mark length is 2T.
In a trellis diagram, a “path” is formed by connecting continuous branches from a given state via another. To consider all possible paths is to consider all possible bit sequences. The most likely path, or “correct path”, can be determined by comparing the signal waveform actually reproduced from the optical storage medium with every ideal waveform expected from the paths to find the ideal waveform that is the closest to the reproduced waveform, that is, the one with the least Euclidean distance from the reproduced waveform.
Now, a Viterbi decoding procedure based on a trellis diagram will be specifically described. At a given time, there are two paths merging at each of states S(O) and S(11), whereas there is a single path coming in to each of S(01) and S(10). Of the two paths merging at S(00) and S(11), retain as the survivor path the one with a less Euclidean distance between the ideal waveform for each path and the reproduced signal waveform. This leaves four paths each terminating at a different one of the four states at a given time. The square of the Euclidean distance between the ideal waveform for the path and the reproduced signal waveform is termed the path metric. The path metric is calculated by summing up branch metrics for all branches making up the path (the branch metric is the square of the difference between the ideal sample level of the branch and the sample level of a reproduced signal waveform.
Let X[t] represent the sample level of the reproduced signal waveform at time t; Ba[t], Bb[t], Bc[t], Bd[t], Be[t], and Bf[t] represent branch metrics for the respective branches a, b, c, d, e, f at time t; and M(00)[t], M(01)[t], M(10)[t], and M(11)[t] represent path metrics for the respective survivor paths leading to states S(00), S(01), S(10), and S(11) at time t. These branch metrics and path metrics are calculated by the following set of equations (1) and (2):Ba[t]=(X[t]+1)^2Bb[t]=Bc[t]=(X[t]+0.5)^2Bd[t]=Be[t]=(X[t]−0.5)^2Bf[t]=(X[t]−1)^2  (1)M(00)[t]=Min{M(00)[t−1]+Ba[t],M(10)[t−1]+Bb[t]}M(01)[t]=M(00)[t−1]+Bc[t]M(10)[t]=M(11)[t−1]+Bd[t]M(11)[t]=Min{M(01)[t−1]+Be[t],M(11)[t−1]+Bf[t]}  (2)
Note that Min{m,n}=m if m≦n and n if m>n.
The process of selecting a smaller path metric from M(00)[t] and M(11)[t] corresponds to the determination of a survivor path.
By repeating the procedure for determining the survivor path every time a sample value for the reproduced signal waveform is received, the path with a greater path metric is removed, so that the number of paths decrements to one. This path is regarded as the correct path so that the original data bit sequence is correctly reproduced.
Here, let us now consider conditions under which Viterbi decoding is correctly done. For the correct path to be ultimately chosen, the path metric must be less for the correct path than for the other path (error path) every time the survivor path is determined. These conditions are expressed by the following set of equations (3):
(3) For a correct bit sequence ending with 000,ΔM=(M(10)[t−1]+Bb[t])−(M(00)[t−1]+Ba[t])>0
For a correct bit sequence ending with 100,ΔM=(M(00)[t−1]+Ba[t])−(M(10)[t−1]+Bb[t])>0
For a correct bit sequence ending with 011,ΔM=(M(11)[t−1]+Bf[t])−(M(01)[t−1]+Be[t])>0
For a correct bit sequence ending with 111,ΔM=(M(01)[t−1]+Be[t])−(M(11)[t−1]+Bf[t])>0
For a correct bit sequence ending with 001 or 110,                ΔM>0 because the survivor path is always determined correctly.        
In the set of equations (3), ΔM is a path metric difference between two paths one of which will be the survivor path. The difference is termed the SAM. To allow no error occurrence, it is required that SAM>0. This fact indicates that error occurrence is increasingly unlikely with increasing SAM value.
A method of evaluating system reliability using SAM is suggested in U.S. Pat. No. 5,938,791 (Date of patent, Aug. 17, 199). According to the method, the reliability of a reproduction device is examined with the standard deviation of the frequency distribution of SAM as an evaluation index.
FIG. 35(a) is a SAM frequency distribution graph prepared from an actual signal reproduced from a (1,7) RLL code sequence recorded on an optical disc. As apparent from these results, a typical SAM distribution has a plurality of peaks. This is because in the calculation of a SAM for all reproduced signals, the Euclidean distance between the correct and error paths differs from one bit sequence to the other.
Now referring to FIG. 35(b), for completely noise-free, ideal reproduced signals from (1,7) RLL code sequences, the SAM frequency distribution shows a plurality of ideal discrete values: namely, 1.5, 2.5, 3.5, 4.5, 5, 6, 7, 8, and 9. The frequencies of the ideal values vary because the ideal values involve different numbers of bit sequences, and the bit sequences occur at different frequencies in the (1,7) RLL code sequences. Actual values deviate from these ideal values due to various noise on the reproduced signal, resulting in multiple distributions being superimposed as shown in FIG. 35(a).
The U.S. Pat. No. 5,938,791 technique generates a SAM distribution as an evaluation index by selecting a bit sequence which, due to noise, yields a SAM<0 at a high probability and a minimum ideal SAM value of (1.5). Although some two or more bit sequences yield the minimum ideal SAM value. The technique however does not distinguish between those bit sequences. In addition, the technique does not use the bit sequences that do not yield the minimum ideal SAM value. Thus, information is insufficient for use in the evaluation of reproduced signals at high accuracy.